SQL ( ∀x / p→q ) & Discrete Mathematics

( ∀x) P ≡ ¬(∃x(¬P))

$(\forall x)P \equiv \neg (\exists x(\neg P))$

$(\forall x)P \equiv \neg (\exists x(\neg P))$

全稱量詞 Universal Quantifier $\forall :$
$\forall xP(x) \iff P(x)$ for all values of $x$ in the (restricted) domain

存在量詞 Existential Quantifier $\exist:$
$\exist xP(x) \iff$ There exists (at least) an element $x$ in the domain such that $P(x)$

德·摩根定律 De Morgan’s Laws for quantifiers:
$\neg \forall xP(x) \equiv \exist x \neg P(x)$

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p→q ≡ ¬p∨q

$p \rightarrow q \equiv \neg p \vee q$

$p \rightarrow q \equiv \neg p \vee q$

蘊涵定律 Implication Law:
$p→q≡¬p∨q$

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REF: https://blog.csdn.net/liteng607/article/details/104649755